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The chords of contact of a point with respect to a hyperbola and its auxillary circle are perpendicular, then the point lies on :A. One of the directricesB. one of the asymptotesC. conjugate hyperbolaD. Axis of hyperbola |
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Answer» Correct Answer - A (i) Let `theta = tan^(-1)2." "x=sin2theta=(2tantheta)/(1+tan^(2)theta)=(4)/(5)` Let `alpha=tan^(-1).(4)/(3), " "y=sin.(alpha)/(2)=sqrt((1-cosalpha)/(2))=sqrt((1-3//5)/(2))=sqrt((1)/(5))` (ii) Take tan on both sides `((3)/(4)+(1)/(7))/(1-(3)/(28))=tan.(pi)/(4)` (iii) Put `x = tan theta. " "therefore 6theta-8theta+4theta=(pi)/(3)impliestheta=(pi)/(6)`. `(because2 thetain "I quadrant"impliessin^(-1)(sin2theta)=2theta,cos^(-1)(cos2theta)=2theta,tan^(-1)(tan2theta)=2theta)` (iv) `tan^(-1)((1)/(5))lttan^(-1)(sqrt(2)-1)" "therefore0lt2tan^(-1)((1)/(5))lt(pi)/(4)` |
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